The Math 122 Midterm Exam is coming up. Suppose the exam scores are normally distributed with a population mean of 73.8% and a standard deviation of 11.3%.

Let's first create a simulation to observe the expected results for a class of Math 122 students. In Excel, create 25 random samples of 23 students each. This means you should have 23 entries in each column, and you should be using columns A - Y. If you need a refresher for creating a random sample that is normally distributed, you can review the Technology Corner from Module 2.

After creating your random samples, copy all the numbers then use the "Paste Values" option in Excel to lock the numbers in place. Save your file, then attach it here:

Now find the mean of each sample.

What is the highest mean?

What is the lowest mean?

Note: While there are no points associated with the attachment or the highest/lowest mean, points will be deducted for not completing this portion or doing it incorrectly. These should be used to help you understand the remainder of the problem.

What is the probability of a student getting a score of 90% or better?  (Round to four decimal places. This should be the theoretical probability that is calculated, NOT the empirical probability from the simulation.)

What is the probability of a class of 23 students having a mean of 90% or better?  (Round to six (6) decimal places.This should be the theoretical probability that is calculated, NOT the empirical probability from the simulation.)

Explain, in your own words, why the answers to these two questions are drastically different. Your explanation should include:

• references to your simulation
• references to your calculations
• common sense explanation

What is the difference between Homeothetic and non homeothetic preference? Derive Engel curve from Income consumption curve for both homeothetc and non homeothetic preferences.

What is the difference between Homeothetic and non homeothetic preference? Derive Engel curve from Income consumption curve for both homeothetc and non homeothetic preferences.

Discuss three non-taxable fringe benefits that companies offer employees and explain why you feel the IRS choose to make these non-taxable to the employee?

Most antimicrobials that arrest protein function are non-selective as to the microbes they affect. Why are they non-selective to the ones they affect? can you give a detailed explanation?

I know what an Electrolyte and a non-electrolyte is, but how do I relate the number of particles in a given solution to the type of solute (electrolyte or non-electrolyte).

What are 2 examples of non-tariff barriers that are considered to be the result of political policy and how can the WTO enforce regulations against non-tariff barriers?

There is a retailer called "The Coop", which carries a wide variety of products with MIT's name and logo: shirts, caps, keychains, pens... you name it! Anything from golf balls and teddy bears to pocket protectors and jewelry. With a store inside MIT's Student Center, and another one in the popular Kendall Square, across the street from MIT campus, The Coop is a favorite stop for casual MIT visitors, current students and their relatives, and nostalgic alumni.

The Coop carries a line of products that feature MIT's official seal cast in a jewelry-grade steel. The same seal (about the size of a coin) is used in multiple finished goods, such as necklaces, tie pins, cufflinks, and paperweights. The Coop is considering introducing in 2018 a new line of products featuring MIT's seal cast in 18 karat gold. These seals would be used in upscale jewelry, and as an ornament in the diploma frames that sell especially during commencement season.

Based on their experience with similar products in the past, The Coop has projected the following demand for gold MIT seals for each month of 2018.

The seals would be produced, under license, by Seventh Seal, a specialty manufacturer of commemorative seals cast in precious metals, located in Syracuse, New York. Seventh Seal has offered to produce the gold MIT seals exclusively for The Coop. Seventh Seal has explained to The Coop that there is a cost to setting up the equipment to produce the gold MIT seal. Because of this, Seventh Seal will charge The Coop a set-up cost of $1417.5 every time the MIT seal is produced.

Because of the high set-up cost, one of the managers at The Coop proposes doing all the seals that will be needed for 2018 in a one-time production batch. "This will save us a lot of money in set-up costs", he says.

Another manager, however, warns that - because the gold seals are expensive - there is an associated holding cost. The Coop estimates that the holding cost will be about $0.21000000000000002 per seal per month (the dot is a decimal mark).

Because of the high holding costs, that manager proposes doing monthly batches in the amount of seals that will be required that month, according to the demand projection. "This will save us a lot of money in holding costs", she says.

What are the total costs (e.g. the sum of set-up costs and holding costs) of producing the gold seals using a lot for lot (or chase) approach and a one time approach?

There is a retailer called "The Coop", which carries a wide variety of products with MIT's name and logo: shirts, caps, keychains, pens... you name it! Anything from golf balls and teddy bears to pocket protectors and jewelry. With a store inside MIT's Student Center, and another one in the popular Kendall Square, across the street from MIT campus, The Coop is a favorite stop for casual MIT visitors, current students and their relatives, and nostalgic alumni.

The Coop carries a line of products that feature MIT's official seal cast in a jewelry-grade steel. The same seal (about the size of a coin) is used in multiple finished goods, such as necklaces, tie pins, cufflinks, and paperweights. The Coop is considering introducing in 2018 a new line of products featuring MIT's seal cast in 18 karat gold. These seals would be used in upscale jewelry, and as an ornament in the diploma frames that sell especially during commencement season.

Based on their experience with similar products in the past, The Coop has projected the following demand for gold MIT seals for each month of 2018.

The seals would be produced, under license, by Seventh Seal, a specialty manufacturer of commemorative seals cast in precious metals, located in Syracuse, New York. Seventh Seal has offered to produce the gold MIT seals exclusively for The Coop. Seventh Seal has explained to The Coop that there is a cost to setting up the equipment to produce the gold MIT seal. Because of this, Seventh Seal will charge The Coop a set-up cost of $1417.5 every time the MIT seal is produced.

Because of the high set-up cost, one of the managers at The Coop proposes doing all the seals that will be needed for 2018 in a one-time production batch. "This will save us a lot of money in set-up costs", he says.

Another manager, however, warns that - because the gold seals are expensive - there is an associated holding cost. The Coop estimates that the holding cost will be about $0.21000000000000002 per seal per month (the dot is a decimal mark).

Because of the high holding costs, that manager proposes doing monthly batches in the amount of seals that will be required that month, according to the demand projection. "This will save us a lot of money in holding costs", she says.

What are the total costs (e.g. the sum of set-up costs and holding costs) of producing the gold seals using a fixed economic order quantity (FOQ) vs periodic order quantity (POQ)?

Prepare the following financial statements based on below info:
1. Balance sheet as on 31 Dec 2017
2. P&L statement for year ending 31 Dec 2018
3. Balance sheet as on 31 Dec 2018
4. Statement of cash flows for the year ending 31 Dec 2018.

Financial Information:
The Company was initially set up by issuing 240,000 shares at an issue price of $1 each.
A factory was at a cost of $500,000.
The new factory was largely financed by taking out a $450,000 mortgage loan. In addition to the mortgage loan, the company took out a $482,000 interest-only unsecured bank loan.
In addition to the factory, the company purchased the following:
Plant&Equipment to the value of $200,000, Furniture&Fixtures to the value of $140,000, Inventory to the value of $184,000.
All these occurred in late Dec 2017. Any cash remaining was put into a bank account.

On 1 Mar 2018, the company took out a bank overdraft. The outstanbding balance on 31 Dec 2018 was $20,000 (This is to be recorded separately from cash balalnce rather than combined.)
On 1 July 2018, motor vehicles to the value of $160,000 were purchased.
On 31 Dec 2018, the company issued corporate bonds to the value of $700,000 and used the proceeds to purchase an additional factory costing $700,000.
On 31 Dec 2018, the company issued 142,000 new ordinary shares at $2 each and 260,000 new preferance shares at $1 each. Some of the amount raised was used to buy additional plant & equipment for the new factory at a cost of $240,000.

During the course of the year ending 31 December 2018, the following transactions occurred.
Products to the value of $1,992,000 were sold & delivered. These sales were m,ade on the basis on one month credit. Of the $1,992,000 in sales occuring in 2018, products to the value of $199,000 were delivered in Dcember 2018 and will not be paid for until January 2019.
Raw materials to the value of $996,000 were ordered and taken delivery of. These purchases were made on the basis of one month's credit. Of the $996,000 in raw materials purchased in 2018, raw materials to the value of $98,000 were ordered and taken delivery of in December 2018 and will not be paid of until Jan 2019.
Payment of wages ($148,000).
Payment of Rent for 2018 ($130,000)
Payment of motor vehicle running expenses ($53,000)
Payment of insurance for 2018 ($49,000)
Payment of interest ($84,000)
Payment for printing & stationery ($30,000)
Payment for Heating & Lighting for 2018 ($31,000)
Payment for Telephone, Postage & internet charges ($20,000)
In addition, an additional $46,000 was paid in December for January's rent.
In addition to the above interest payment, the principle owing on the mortgage loan was reduced by $42,000.
The value of inventory on 31 Dec 2018 was $213,000.

Additional Info : Depreciation on motor vehicles, plant&equipment and furniture&fixtures is calculated on a straight-line basis at the rate of 10% per year.
The company faces a tax rate of 20% . The company's Dividend payout ratio is 75%.